混合趋化模型中的行波
Travelling waves in hybrid chemotaxis models
摘要：
趋化性的混合模型结合了基于代理的细胞模型和细胞外化学信号的偏微分方程模型。本文研究了细菌趋药性混合模型的行波性质。使用基于代理（基于个体）的方法与描述信号转导的内部动力学对细菌进行建模。除了细菌的趋化行为外，基于个体的模型还包括细胞增殖和死亡。细胞消耗细胞外营养场（化学引诱物），这是使用偏微分方程建模。介观和宏观方程表示的混合模型的行为，推导出这些模型的行波解的存在性。结果表明，细胞增殖是必要的混合模型中的非瞬态（平稳）行波的存在。此外，连续模型和混合模型的波速之间的数值比较显示出良好的协议的情况下，弱趋药性和定性协议的强趋药性的情况下。在缓慢的细胞适应的情况下，我们检测到振荡行为的波，这是不能解释的平均场近似。
英文摘要：
Hybrid models of chemotaxis combine agent-based models of cells with partial differential equation models of extracellular chemical signals. In this paper, travelling wave properties of hybrid models of bacterial chemotaxis are investigated. Bacteria are modelled using an agent-based (individual-based) approach with internal dynamics describing signal transduction. In addition to the chemotactic behaviour of the bacteria, the individual-based model also includes cell proliferation and death. Cells consume the extracellular nutrient field (chemoattractant) which is modelled using a partial differential equation. Mesoscopic and macroscopic equations representing the behaviour of the hybrid model are derived and the existence of travelling wave solutions for these models is established. It is shown that cell proliferation is necessary for the existence of non-transient (stationary) travelling waves in hybrid models. Additionally, a numerical comparison between the wave speeds of the continuum models and the hybrid models shows good agreement in the case of weak chemotaxis and qualitative agreement for the strong chemotaxis case. In the case of slow cell adaptation, we detect oscillating behaviour of the wave, which cannot be explained by mean-field approximations.
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